The exponent is not determined by dimensional considerations in so-called self-similar solutions of the second kind [1]}. Such a solution was first discovered by Guderley [2]} who found that the spherical shock wave disappearing at time \(t=0\)  shrinks as \((-t)^b\)  with exponent \(b\)  not fixed by dimensional analysis. This problem (and its deformations) is still explored [3]}, [4]}. See [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]} for other self-similar solutions of the second kind. Their importance in physics is also clear [12]}.
<FIGURE><FIGURE>